%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP321-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:29 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 55
% Syntax : Number of formulae : 332 ( 19 unt; 22 def)
% Number of atoms : 1051 ( 302 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1356 ( 637 ~; 697 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,sk_c7) != sk_c6
| inverse(X4) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(sk_c6,sk_c7) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f71,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl0_2
<=> ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f76,f73,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f90,f69]) ).
fof(f95,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f90,f95]) ).
fof(f100,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f102,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f90,f100]) ).
fof(f105,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f107,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f90,f105]) ).
fof(f110,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f90,f110]) ).
fof(f115,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f115,f69]) ).
fof(f119,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f115,f95]) ).
fof(f120,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f115,f100]) ).
fof(f121,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f115,f105]) ).
fof(f122,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f115,f110]) ).
fof(f124,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f124,f69]) ).
fof(f128,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f124,f95]) ).
fof(f129,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f124,f100]) ).
fof(f130,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f124,f105]) ).
fof(f131,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f124,f110]) ).
fof(f133,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_1
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f133,f69]) ).
fof(f137,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f133,f95]) ).
fof(f138,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f133,f100]) ).
fof(f139,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f133,f105]) ).
fof(f140,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f133,f110]) ).
fof(f142,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_1
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f142,f69]) ).
fof(f146,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f142,f95]) ).
fof(f147,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f142,f100]) ).
fof(f148,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f142,f105]) ).
fof(f149,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f142,f110]) ).
fof(f150,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f69]) ).
fof(f152,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f100]) ).
fof(f153,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f105]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f110]) ).
fof(f155,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f156,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f135]) ).
fof(f158,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_15 ),
inference(superposition,[],[f4,f144]) ).
fof(f161,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_6 ),
inference(superposition,[],[f4,f86]) ).
fof(f164,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c2,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c2,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f167,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f158,f1]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f174,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f171,f126]) ).
fof(f194,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f86,f174]) ).
fof(f195,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f117,f174]) ).
fof(f225,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f167,f144]) ).
fof(f230,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_14 ),
inference(superposition,[],[f167,f156]) ).
fof(f232,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f167,f155]) ).
fof(f235,plain,
( sk_c2 = multiply(inverse(sk_c7),identity)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f232,f174]) ).
fof(f240,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f225,f174]) ).
fof(f247,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f240,f135]) ).
fof(f254,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c8,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f160,f247]) ).
fof(f257,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f254,f174]) ).
fof(f258,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f257,f194]) ).
fof(f259,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f258,f144]) ).
fof(f260,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f259,f174]) ).
fof(f264,plain,
( sk_c1 = sk_c2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f235,f230]) ).
fof(f266,plain,
( sk_c3 = multiply(sk_c1,sk_c8)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f117,f264]) ).
fof(f275,plain,
( multiply(sk_c1,sk_c7) = sk_c3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f266,f174]) ).
fof(f279,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f275,f144]) ).
fof(f280,plain,
( sk_c7 = sk_c3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f279,f174]) ).
fof(f281,plain,
( sk_c8 != multiply(sk_c7,sk_c7)
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f71,f260]) ).
fof(f282,plain,
( sk_c7 != sk_c8
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f281,f247]) ).
fof(f283,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f282,f174]) ).
fof(f284,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f283]) ).
fof(f286,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f74,f260]) ).
fof(f288,plain,
( sk_c7 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f286,f144]) ).
fof(f304,definition,
( spl0_17
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f305,plain,
( identity = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f310,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f288,f174]) ).
fof(f312,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f310,f135]) ).
fof(f313,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f312]) ).
fof(f314,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f77,f174]) ).
fof(f315,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f314,f174]) ).
fof(f323,plain,
( sk_c7 != sk_c3
| sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f315,f195]) ).
fof(f333,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f323,f280]) ).
fof(f336,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f333,f264]) ).
fof(f339,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f336,f135]) ).
fof(f340,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f378,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f83,f174]) ).
fof(f382,plain,
( sk_c7 != sk_c3
| sk_c7 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f378,f195]) ).
fof(f392,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f382,f280]) ).
fof(f395,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f392,f264]) ).
fof(f398,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f395,f135]) ).
fof(f399,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f406,definition,
( spl0_20
<=> sk_c7 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f416,definition,
( spl0_22
<=> sk_c7 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f417,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f428,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f107,f174]) ).
fof(f429,plain,
( sk_c7 = multiply(sk_c4,sk_c7)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f112,f174]) ).
fof(f431,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f70,f174]) ).
fof(f435,definition,
( spl0_24
<=> sk_c7 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f436,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f439,plain,
( spl0_24
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f431,f124,f115,f90,f69,f435]) ).
fof(f444,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f167,f102]) ).
fof(f445,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f102]) ).
fof(f446,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f444,f97]) ).
fof(f447,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f446,f100,f95,f406]) ).
fof(f498,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f74,f429]) ).
fof(f499,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f74,f102]) ).
fof(f505,plain,
( sk_c7 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f499]) ).
fof(f508,definition,
( spl0_25
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f509,plain,
( sk_c7 = sk_c6
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f519,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f505,f97]) ).
fof(f520,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f521,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f498,f428]) ).
fof(f523,plain,
( ~ spl0_25
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f521,f124,f115,f110,f105,f90,f73,f508]) ).
fof(f554,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f167,f112]) ).
fof(f555,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f112]) ).
fof(f556,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f554,f107]) ).
fof(f557,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f77,f107]) ).
fof(f562,plain,
( sk_c7 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f557]) ).
fof(f568,definition,
( spl0_28
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f569,plain,
( sk_c7 = sk_c8
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f577,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f562,f112]) ).
fof(f578,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f580,plain,
( sk_c7 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f80,f97]) ).
fof(f582,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f80,f92]) ).
fof(f583,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f582]) ).
fof(f591,definition,
( spl0_31
<=> sk_c7 = multiply(sk_c8,multiply(sk_c5,sk_c8)) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f593,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| spl0_31 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f594,plain,
( ~ spl0_31
| ~ spl0_28
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f580,f95,f79,f568,f591]) ).
fof(f596,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_22 ),
inference(superposition,[],[f167,f417]) ).
fof(f605,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f583,f165]) ).
fof(f612,plain,
( sk_c7 = sk_c8
| ~ spl0_1
| ~ spl0_24 ),
inference(superposition,[],[f70,f436]) ).
fof(f619,plain,
( ~ spl0_28
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f605,f90,f79,f568]) ).
fof(f620,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f612,f435,f69,f568]) ).
fof(f623,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c7)
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f445,f417]) ).
fof(f631,plain,
( sk_c8 = multiply(sk_c5,sk_c7)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_demodulation,[],[f623,f70]) ).
fof(f654,plain,
( multiply(sk_c4,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f555,f556]) ).
fof(f655,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c6,sk_c7)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f161,f556]) ).
fof(f658,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f655,f70]) ).
fof(f660,plain,
( sk_c8 = sk_c6
| ~ spl0_1
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f631,f102]) ).
fof(f662,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c8)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f167,f631]) ).
fof(f664,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_demodulation,[],[f662,f97]) ).
fof(f676,plain,
( sk_c7 = sk_c8
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f664,f658]) ).
fof(f679,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f86,f664]) ).
fof(f686,plain,
( spl0_25
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f679,f416,f100,f95,f85,f69,f508]) ).
fof(f693,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f654,f112]) ).
fof(f694,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f693,f110,f105,f416]) ).
fof(f697,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f676,f416,f110,f105,f100,f95,f85,f69,f568]) ).
fof(f700,plain,
( sk_c7 != sk_c7
| sk_c8 != multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f83,f97]) ).
fof(f704,plain,
( sk_c8 != multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f700]) ).
fof(f727,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c5,sk_c7))
| ~ spl0_28
| spl0_31 ),
inference(superposition,[],[f593,f569]) ).
fof(f730,plain,
( sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_9
| ~ spl0_28
| spl0_31 ),
inference(forward_demodulation,[],[f727,f102]) ).
fof(f732,plain,
( ~ spl0_20
| ~ spl0_9
| ~ spl0_28
| spl0_31 ),
inference(avatar_split_clause,[],[f730,f591,f568,f100,f406]) ).
fof(f743,plain,
( sk_c7 != multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_28 ),
inference(forward_demodulation,[],[f704,f569]) ).
fof(f752,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_28 ),
inference(superposition,[],[f743,f102]) ).
fof(f753,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_25
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f752,f509]) ).
fof(f754,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f753]) ).
fof(f759,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_9
| ~ spl0_22
| ~ spl0_28 ),
inference(forward_demodulation,[],[f660,f569]) ).
fof(f761,plain,
( spl0_25
| ~ spl0_1
| ~ spl0_9
| ~ spl0_22
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f759,f568,f416,f100,f69,f508]) ).
fof(f785,plain,
( identity = sk_c7
| ~ spl0_22 ),
inference(superposition,[],[f3,f596]) ).
fof(f789,plain,
( spl0_17
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f785,f416,f304]) ).
fof(f793,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_17 ),
inference(superposition,[],[f1,f305]) ).
fof(f800,plain,
( sk_c8 != sk_c6
| spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f87,f793]) ).
fof(f807,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f800,f660]) ).
fof(f808,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f807]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f93]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f103]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f108]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl0_1
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s22,plain,
( spl0_1
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f284]) ).
cnf(s34,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f313]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f340]) ).
cnf(s43,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f399]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_24 ),
inference(sat_conversion,[],[f439]) ).
cnf(s51,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_20 ),
inference(sat_conversion,[],[f447]) ).
cnf(s71,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f520]) ).
cnf(s72,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_25 ),
inference(sat_conversion,[],[f523]) ).
cnf(s85,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f578]) ).
cnf(s87,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_28
| ~ spl0_31 ),
inference(sat_conversion,[],[f594]) ).
cnf(s90,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_28 ),
inference(sat_conversion,[],[f619]) ).
cnf(s91,plain,
( ~ spl0_1
| ~ spl0_24
| spl0_28 ),
inference(sat_conversion,[],[f620]) ).
cnf(s93,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22
| spl0_25 ),
inference(sat_conversion,[],[f686]) ).
cnf(s97,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f694]) ).
cnf(s98,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22
| spl0_28 ),
inference(sat_conversion,[],[f697]) ).
cnf(s109,plain,
( ~ spl0_9
| ~ spl0_20
| ~ spl0_28
| spl0_31 ),
inference(sat_conversion,[],[f732]) ).
cnf(s111,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f754]) ).
cnf(s113,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_22
| spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f761]) ).
cnf(s116,plain,
( spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f789]) ).
cnf(s118,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f808]) ).
cnf(s119,plain,
spl0_1,
inference(rat,[],[s32,s2,s7,s12,s17,s22,s27]) ).
cnf(s120,plain,
( ~ spl0_9
| ~ spl0_22
| spl0_6 ),
inference(rat,[],[s116,s118,s119]) ).
cnf(s121,plain,
spl0_6,
inference(rat,[],[s120,s97,s29,s30,s31]) ).
cnf(s122,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s43,s11,s16,s21,s26]) ).
cnf(s123,plain,
( ~ spl0_7
| spl0_22
| ~ spl0_5 ),
inference(rat,[],[s43,s10,s15,s20,s25,s97,s122]) ).
cnf(s124,plain,
( spl0_22
| ~ spl0_5 ),
inference(rat,[],[s97,s5,s6,s123]) ).
cnf(s125,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s111,s98,s93,s124,s119,s121]) ).
cnf(s126,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s43,s8,s13,s18,s23]) ).
cnf(s127,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s43,s10,s15,s20,s25,s125,s126,s122]) ).
cnf(s128,plain,
( ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s125,s3,s5,s6,s127]) ).
cnf(s129,plain,
~ spl0_5,
inference(rat,[],[s43,s4,s9,s14,s19,s24,s128]) ).
cnf(s130,plain,
( spl0_11
| spl0_24
| ~ spl0_7 ),
inference(rat,[],[s50,s11,s16,s119]) ).
cnf(s131,plain,
( spl0_13
| ~ spl0_10
| ~ spl0_11
| spl0_28 ),
inference(rat,[],[s98,s13,s14,s97,s119,s121]) ).
cnf(s132,plain,
( ~ spl0_10
| spl0_28
| ~ spl0_7 ),
inference(rat,[],[s98,s8,s9,s50,s131,s97,s130,s91,s119,s121]) ).
cnf(s133,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s50,s10,s15,s132,s91,s90,s119]) ).
cnf(s134,plain,
~ spl0_4,
inference(rat,[],[s87,s109,s98,s51,s97,s3,s4,s5,s6,s133,s119,s121]) ).
cnf(s135,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s11,s16,s21,s26]) ).
cnf(s136,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s10,s15,s20,s25,s85,s135]) ).
cnf(s137,plain,
~ spl0_3,
inference(rat,[],[s85,s5,s6,s136]) ).
cnf(s138,plain,
spl0_2,
inference(rat,[],[s1,s121,s119,s129,s134,s137]) ).
cnf(s139,plain,
spl0_13,
inference(rat,[],[s71,s13,s14,s138]) ).
cnf(s140,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_7 ),
inference(rat,[],[s34,s19,s24,s113,s72,s132,s97,s138,s121,s139,s119]) ).
cnf(s141,plain,
spl0_12,
inference(rat,[],[s71,s8,s9,s138]) ).
cnf(s142,plain,
( spl0_11
| ~ spl0_7 ),
inference(rat,[],[s34,s21,s26,s138,s121,s139,s141]) ).
cnf(s143,plain,
( ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s34,s20,s25,s140,s141,s139,s121,s138]) ).
cnf(s144,plain,
~ spl0_7,
inference(rat,[],[s143,s142]) ).
cnf(s147,plain,
spl0_9,
inference(rat,[],[s4,s144]) ).
cnf(s148,plain,
spl0_8,
inference(rat,[],[s3,s144]) ).
cnf(s150,plain,
$false,
inference(rat,[],[s71,s138,s147,s148]) ).
fof(f812,plain,
$false,
inference(avatar_sat_refutation,[],[s150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP321-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:52:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % (2588525)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (2588531)% WARNING: option uhcvi not known.
% 0.09/0.45 % (2588530)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4010921472_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (2588532)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3355197081:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (2588533)dis+10_1_sil=32000:sp=arity:random_seed=1587327664:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (2588531)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3936800028:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.45 % (2588534)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3800478861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (2588535)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=365157141:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (2588536)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1041600360:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % TRYING [4]
% 0.09/0.45 % (2588531) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2588525-2588531"...
% 0.09/0.45 % (2588534) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2588525-2588534"...
% 0.09/0.45 % (2588533) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2588525-2588533"...
% 0.09/0.45 % (2588531)...printing done.
% 0.09/0.45 % (2588531)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (2588531)------------------------------
% 0.09/0.45 % (2588531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (2588531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (2588531)CaDiCaL version: 2.1.3
% 0.09/0.45 % (2588531)Termination reason: Refutation
% 0.09/0.45 % (2588531)Time elapsed: 0.014 s
% 0.09/0.45 % (2588531)Peak memory usage: 13 MB
% 0.09/0.45 % (2588531)Instructions burned: 31 (million)
% 0.09/0.45 % (2588525)Success in time 0.047 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------